Can I apply for a residence permit for a private house here in Qianqiao, Huishan District?

Of course. According to the Regulations of People's Republic of China (PRC) on Residence Permit, all permanent residents living in this city can apply for residence permit. Therefore, those who live in private houses in Qianqiao, Huishan District, and can provide valid identification, housing lease contract or real estate license and other necessary materials, can submit a residence permit application to the local police station (community police office).